How do I kill religious units

[Synergy2525]

I’m still learning this game. I’m on turn 160 and I now have these religious units on my island taking away -250 Catholicism for +250 Buddhism. How do I kill these units?

[Kotli]

They are religious units as such you need your own religious units (brought with faith) to fight them off.
Apostles and Inquisitors to attack (only religious units that can attack) and gurus to heal them back up.
You can use Inquisitors to remove Heresy (that is remove other religions from your cities).

[tempest.of.emptiness]

Religious units can spread religion, but that -250 Catholicism you are seeing is happening because Buddhist religious units are fighting and defeating Catholic religious units. So, you should be able to watch what is happening to see an example of how a religious unit can die.

There are two main ways to kill a religious unit. First, if you are at war with the owner of the religious unit, you can move a military unit into the same hex as the enemy religious unit and use the "Condemn Heretic" action to eliminate the unit. Second, if you have advanced (ie not missionaries) religious units of your own you can fight the enemy religious units to try to defeat them. This does not require you to be at war with the owner of the other religious unit, but it does require that the other unit follow another religion. Also, both units take damage in the battle, so there is a possibility that your unit might die instead of the enemy. You should try to avoid this outcome if at all possible, by choosing your battles carefully and by healing your wounded religious units adjacent to one of your holy sites.

[Sarisin]

One interesting thing is disasters will not kill religious units - same for Great People and Traders, I think.

[captainpatch]

A decent strategy that I have used works like this:

1) Build Wonders and buildings that increase the number of charges your religious units have.
2) Use policies that improve religious units theological combat strength and adds unit charges.
3) When using an Apostle, ALWAYS leave him with at least one charge.
4) Build LOTS of Apostles.
5) As your Apostles get worn down from theological combat, you can run them back to any of your cities with a Holy Site. Placing the wounded on or adjacent to the Holy Site allows it to heal. After a couple/few turns, the unit should be fully healed, ready to sally forth to crush and kill heathens and pagans once more.

As far as I can see, the AI doesn't bother to save one charge to keep a theological unit alive, nor run back to Holy Sites to heal.

It might be that you run into enemy Apostles with @130 combat strength, while your best unit is just a 118 or so. Head-to-head, you WILL lose in combat almost always. But if you have, say, 5 Apostles in close proximity, hitting that unit one after another will wear it down. At least enough that attack # 5 kills it. Then all your wounded Apostles run back home to heal. Thereafter, that "wolfpack" can go hunting for other large-value enemy Apostles.

[Shikabane屍]

Could always declare a bunch of wars on the people leading the religions and condemn heretic with your actual army. I've used this a few times to stop people from getting a religious win in my empire